Code.No: 25058

RR

SET-1

or ld

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD III.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 AERODYNAMICS – II (AERONAUTICAL ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks --1.a) What is substantial derivative? Explain its physical significance and derive a suitable expression for it. b) Define the following with respect to velocity field. i) Divergence ii) Curl Obtain suitable mathematical correlations for them. [8+8]

What is circulation? Explain its significance in theoretical aerodynamics. Consider a two dimensional incompressible, inviscid, irrotational flow with u and v as its cy −cx velocity components in the velocity field given by u = 2 and v= 2 2 x +y x + y2 where ‘c’ is a constant. Obtain the equation of streamline passing through (0, 8). [8+8]

3.a)

Explain the significance of Laplace’s equation stating the assumptions involved in it, using suitable correlations. Consider a venture with a throat-to-inlet area ratio of 0.65, mounted on the side of an airplane fuselage. Considering that the airplane is flying at standard sea level with Pstat

b)

uW

2.a) b)

at throat as 1800 N / m 2 , determine the velocity of the airplane. 4.a)

What are Vortex flows? Derive suitable relations for the stream function and potential function. A circular cylinder of radius ‘R’ is experiencing non-lifting flow over it, with a stream velocity V∞ = 12 m / s . Do the shapes of the streamlines change if V∞ is Comment and justify your answer. [8+8]

velocity free doubled.

nt

b)

[8+8]

5.a)

Aj

b)

Define an airfoil. Explain the characteristics such as lift and drag variations with reference to angle of attack using suitable sketches. Considering potential flow over a rotating cylinder, derive the Kutta-Joukowski theorem using suitable equations/expressions. [8+8]

6.a)

From the theory of thin airfoils, prove that for a cambered airfoil the location of

⎛ c ⎞⎡ ⎛ π = X pressure cp ⎜ ⎟ ⎢1 + ⎜ ⎝ 4 ⎠ ⎣ ⎝ cA

⎤ ⎞ − ( A A ) ⎟ 1 2 ⎥ ⎠ ⎦

1

center of

Derive suitable expressions for lift, coefficient of lift, moment coefficient and slope of the lift curve for a circular arc airfoil whose circulation distribution is given as [1 + cos θ ] ⎪⎫ + 4β V sin θ ⎪⎧ [8+8] Γ = ⎨2V∞α ⎬ ∞ sin θ ⎪⎭ ⎪⎩

7.a) b)

Explain the philosophy of Prandtl’s lifting line theory and derive its fundamental equation. Enumerate the significance of elliptical lift distribution. Derive the aerodynamic characteristics of a finite wing experiencing above type of distribution. [8+8]

8.

A tapered wing of span ‘b’ is experiencing a modified elliptical distribution

.in

b)

⎡ ⎛ 2 y ⎞⎤ ⎡ ⎛ 2 y ⎞⎤ given by the expression as Γ( y ) = Γ 0 ⎢1 − ⎜ 2 ⎟ ⎥ ⎢1 + 0.8 ⎜ 2 ⎟ ⎥ ⎝ b ⎠⎦ ⎣ ⎝ b ⎠⎦ ⎣ Derive suitable correlations to estimate i) Downwash ii) Induced drag and iii) Total lift. 2

Aj

nt

uW

or ld

2

2

loading

[16]

Code.No: 25058

SET-2

RR

1.a) b)

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD III.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 AERODYNAMICS – II (AERONAUTICAL ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

Explain the significance of Laplace’s equation stating the assumptions involved in it, using suitable correlations. Consider a venture with a throat-to-inlet area ratio of 0.65, mounted on the side of an airplane fuselage. Considering that the airplane is flying at standard sea level with Pstat at throat as 1800 N / m 2 , determine the velocity of the airplane.

3.a) b)

4.a)

or ld

b)

What are Vortex flows? Derive suitable relations for the stream function and potential function. A circular cylinder of radius ‘R’ is experiencing non-lifting flow over it, with a stream velocity V∞ = 12 m / s . Do the shapes of the streamlines change if V∞ is Comment and justify your answer. [8+8]

velocity free doubled.

Define an airfoil. Explain the characteristics such as lift and drag variations with reference to angle of attack using suitable sketches. Considering potential flow over a rotating cylinder, derive the Kutta-Joukowski theorem using suitable equations/expressions. [8+8]

uW

2.a)

[8+8]

From the theory of thin airfoils, prove that for a cambered airfoil the location of

center of

⎤ ⎛ c ⎞⎡ ⎛ π ⎞ 1 + ( A − A ) ⎢ ⎜ ⎟ 1 2 ⎥ ⎟ ⎝ 4 ⎠ ⎣ ⎝ cA ⎠ ⎦

pressure X cp = ⎜

Derive suitable expressions for lift, coefficient of lift, moment coefficient and slope of the lift curve for a circular arc airfoil whose circulation distribution is given as [1 + cos θ ] ⎪⎫ + 4β V sin θ ⎪⎧ [8+8] Γ = ⎨2V∞α ⎬ ∞ sin θ ⎪⎭ ⎪⎩

nt

b)

Explain the philosophy of Prandtl’s lifting line theory and derive its fundamental equation. Enumerate the significance of elliptical lift distribution. Derive the aerodynamic characteristics of a finite wing experiencing above type of distribution. [8+8]

Aj

5.a) b)

6.

A tapered wing of span ‘b’ is experiencing a modified elliptical distribution

⎡ ⎛ 2 y ⎞⎤ ⎡ ⎛ 2 y ⎞⎤ given by the expression as Γ( y ) = Γ 0 ⎢1 − ⎜ 2 ⎟ ⎥ ⎢1 + 0.8 ⎜ 2 ⎟ ⎥ ⎝ b ⎠⎦ ⎣ ⎝ b ⎠⎦ ⎣ 2

3

2

loading

Derive suitable correlations to estimate i) Downwash ii) Induced drag and iii) Total lift.

b)

What is circulation? Explain its significance in theoretical aerodynamics. Consider a two dimensional incompressible, inviscid, irrotational flow with u and v as its cy −cx velocity components in the velocity field given by u = 2 and v= 2 2 x +y x + y2 where ‘c’ is a constant. Obtain the equation of streamline passing through (0, 8). [8+8]

Aj

nt

uW

or ld

8.a) b)

What is substantial derivative? Explain its physical significance and derive a suitable expression for it. Define the following with respect to velocity field. i) Divergence ii) Curl Obtain suitable mathematical correlations for them. [8+8]

.in

7.a)

[16]

4

Code.No: 25058

SET-3

RR

b)

2.a)

Define an airfoil. Explain the characteristics such as lift and drag variations with reference to angle of attack using suitable sketches. Considering potential flow over a rotating cylinder, derive the Kutta-Joukowski theorem using suitable equations/expressions. [8+8] From the theory of thin airfoils, prove that for a cambered airfoil the location of

or ld

1.a)

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD III.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 AERODYNAMICS – II (AERONAUTICAL ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

center of

⎤ ⎛ c ⎞⎡ ⎛ π ⎞ + − 1 ( A A ) ⎢ ⎜ ⎟ 1 2 ⎥ ⎟ ⎝ 4 ⎠ ⎣ ⎝ cA ⎠ ⎦

pressure X cp = ⎜

Derive suitable expressions for lift, coefficient of lift, moment coefficient and slope of the lift curve for a circular arc airfoil whose circulation distribution is given as [1 + cos θ ] ⎪⎫ + 4β V sin θ ⎪⎧ [8+8] Γ = ⎨2V∞α ⎬ ∞ sin θ ⎪⎭ ⎪⎩

3.a) b)

Explain the philosophy of Prandtl’s lifting line theory and derive its fundamental equation. Enumerate the significance of elliptical lift distribution. Derive the aerodynamic characteristics of a finite wing experiencing above type of distribution. [8+8]

4.

A tapered wing of span ‘b’ is experiencing a modified elliptical distribution

uW

b)

⎡ ⎛ 2 y ⎞⎤ ⎡ ⎛ 2 y ⎞⎤ given by the expression as Γ( y ) = Γ 0 ⎢1 − ⎜ 2 ⎟ ⎥ ⎢1 + 0.8 ⎜ 2 ⎟ ⎥ ⎝ b ⎠⎦ ⎣ ⎝ b ⎠⎦ ⎣ Derive suitable correlations to estimate i) Downwash ii) Induced drag and iii) Total lift.

nt

2

b)

[16]

What is substantial derivative? Explain its physical significance and derive a suitable expression for it. Define the following with respect to velocity field. i) Divergence ii) Curl Obtain suitable mathematical correlations for them. [8+8]

Aj

5.a)

loading

2

5

What is circulation? Explain its significance in theoretical aerodynamics. Consider a two dimensional incompressible, inviscid, irrotational flow with u and v as its cy −cx velocity components in the velocity field given by u = 2 and v= 2 2 x +y x + y2 where ‘c’ is a constant. Obtain the equation of streamline passing through (0, 8). [8+8]

7.a)

Explain the significance of Laplace’s equation stating the assumptions involved in it, using suitable correlations. Consider a venture with a throat-to-inlet area ratio of 0.65, mounted on the side of an airplane fuselage. Considering that the airplane is flying at standard sea level with Pstat

b)

at throat as 1800 N / m 2 , determine the velocity of the airplane.

What are Vortex flows? Derive suitable relations for the stream function and potential function. A circular cylinder of radius ‘R’ is experiencing non-lifting flow over it, with a stream velocity V∞ = 12 m / s . Do the shapes of the streamlines change if V∞ is Comment and justify your answer. [8+8]

Aj

nt

uW

b)

[8+8]

or ld

8.a)

.in

6.a) b)

6

velocity

free doubled.

Code.No: 25058

SET-4

RR

.in

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD III.B.TECH - I SEMESTER SUPPLEMENTARY EXAMINATIONS NOVEMBER, 2009 AERODYNAMICS – II (AERONAUTICAL ENGINEERING) Time: 3hours Max.Marks:80 Answer any FIVE questions All questions carry equal marks ---

Explain the philosophy of Prandtl’s lifting line theory and derive its fundamental equation. Enumerate the significance of elliptical lift distribution. Derive the aerodynamic characteristics of a finite wing experiencing above type of distribution. [8+8]

2.

A tapered wing of span ‘b’ is experiencing a modified elliptical distribution

or ld

1.a) b)

⎡ ⎛ 2 y ⎞⎤ ⎡ ⎛ 2 y ⎞⎤ given by the expression as Γ( y ) = Γ 0 ⎢1 − ⎜ 2 ⎟ ⎥ ⎢1 + 0.8 ⎜ 2 ⎟ ⎥ ⎝ b ⎠⎦ ⎣ ⎝ b ⎠⎦ ⎣ Derive suitable correlations to estimate i) Downwash ii) Induced drag and iii) Total lift. 2

b)

What is circulation? Explain its significance in theoretical aerodynamics. Consider a two dimensional incompressible, inviscid, irrotational flow with u and v as its cy −cx velocity components in the velocity field given by u = 2 and v= 2 2 x +y x + y2 where ‘c’ is a constant. Obtain the equation of streamline passing through (0, 8). [8+8] Explain the significance of Laplace’s equation stating the assumptions involved in it, using suitable correlations. Consider a venture with a throat-to-inlet area ratio of 0.65, mounted on the side of an airplane fuselage. Considering that the airplane is flying at standard sea level with Pstat

nt

4.a) b)

5.a)

Aj

b)

[16]

What is substantial derivative? Explain its physical significance and derive a suitable expression for it. Define the following with respect to velocity field. i) Divergence ii) Curl Obtain suitable mathematical correlations for them. [8+8]

uW

3.a)

loading

2

at throat as 1800 N / m 2 , determine the velocity of the airplane.

7

[8+8]

7.a) b)

8.a)

free doubled.

Define an airfoil. Explain the characteristics such as lift and drag variations with reference to angle of attack using suitable sketches. Considering potential flow over a rotating cylinder, derive the Kutta-Joukowski theorem using suitable equations/expressions. [8+8] From the theory of thin airfoils, prove that for a cambered airfoil the location of

⎛ c ⎞⎡ ⎛ π = X pressure cp ⎜ ⎟ ⎢1 + ⎜ ⎝ 4 ⎠ ⎣ ⎝ cA

⎤ ⎞ − ( A A ) ⎟ 1 2 ⎥ ⎠ ⎦

center of

Derive suitable expressions for lift, coefficient of lift, moment coefficient and slope of the lift curve for a circular arc airfoil whose circulation distribution is given as ⎧⎪ [1 + cos θ ] ⎫⎪ + 4β V sin θ [8+8] Γ = ⎨2V∞α ⎬ ∞ sin θ ⎭⎪ ⎩⎪

Aj

nt

uW

b)

velocity

.in

b)

What are Vortex flows? Derive suitable relations for the stream function and potential function. A circular cylinder of radius ‘R’ is experiencing non-lifting flow over it, with a stream velocity V∞ = 12 m / s . Do the shapes of the streamlines change if V∞ is Comment and justify your answer. [8+8]

or ld

6.a)

8